7. 1. Factorizing single brackets
Factorizing example using single brackets
To factorize fully: 3x+6
# Find the highest common factor (HCF) of the numbers 3 (the coefficient of x) and 6 (the
constant).
Factors of 3: 1,3
Factors of 6: 1,2,3,6
# Write the highest common factor (HCF) at the front of the single bracket.
3( )
#Fill in each term in the bracket by multiplying out.
What do I need to multiply 3 by to give me 3x?
3×x=3x
What do I need to multiply 3 by to give me 6?
3×2=6
So , 3(x+2)
We can check the answer by multiplying out the bracket!
3(x+2)=3x+6
8. 2a) Factorizing quadratics into double brackets: x2 + bx + c
To factorize: x2+6x+5
# Write out the factor pairs of the last number 5.
Factors of 5: 1, 5
2 #Find a pair of factors that (+) to give the middle number (6) and( ✕) to give
the last number (5).
1 + 5 = 6 ✔ 1 ✕ 5 = 5 ✔
# Write two brackets and put the variable at the start of each one.
(x )(x )
# Write one factor in the first bracket and the other factor in the second
bracket. The order isn’t important, the signs of the factors are.
(x+1)(x+5)
9. 2b) Factorizing quadratics into double brackets: ax2 + bx + c
To factorize: 2x2+5x+3
# Multiply the end numbers together (2 and 3) then write out the factor pairs of this
new number in order
Factors of 6: 1, 2, 3,6
2 We need a pair of factors that + to give the middle number (5) and ✕ to give this new
number (6)
2 + 3 = 5 ✔
2 ✕ 3 = 6 ✔
3 Rewrite the original expression, this time splitting the middle term into the two factors
we found in step 2.
2x2+2x+3x+3
4 Split the equation down the middle and factorise fully each half.
2x(x+1)+3(x+1)
5 Factorise the whole expression by bringing whatever is in the bracket to the front and
writing the two other terms in the other bracket.
(2x+3)(x+1)
10. 3. Difference of two squares
To factorize fully: 4𝑥2-9
1.Write down 2 brackets.
( )( )
#Square root the first term and write it on the left-hand side of both brackets.
4𝑥2 =2x
(2x )(2x )
Square root the last term and write it on the right-hand side of both brackets.
√9=±3
(2x 3)(2x 3)
4 Put + in the middle of one bracket and – in the middle of the other (the order
doesn’t matter).
(2x+3)(2x−3)
